2025-07-25 –, Main Room 2
Elastic networks composed of Hookean springs serve as important models for the cytoskeleton, enzymes, and adaptive metamaterials. However, the elastic moduli of such networks are typically computed with finite difference methods, which yield inexact results that may introduce significant errors for mechanically sensitive materials. In ElasticityAD.jl, we have use Julia's automatic differentiation framework to enable calculations of exact stiffness tensor and elastic moduli.
ElasticityAD.jl: EXACT linear response of elastic networks based on automatic differentiation
Elastic networks are stiff yet lightweight with low volume fractions. Thus, they appear in many biological and engineering contexts, e.g. as mechanical scaffolds in the cytoskeleton. The usual way to compute their stiffness tensor is through finite differences, i.e., give the material a small deformation, minimize the energy, and find the difference in energy before and after the deformation. This is inexact and can introduce large errors if the deformation is not chosen small enough, but on the other hand, this deformation cannot be chosen too small compared to the precision threshold during the energy minimization. Automatic differentiation is an excellent solution to this problem. We have built a package based on exactly this idea. One can now obtain exact stiffness tensor and elastic moduli. Our package builds Network objects that incorporate julia Graphs and coordinates of the nodes, as well es the rest lengths of edges.
Haina obtained her B.S. in chemistry and mathematics at National University of Singapore in 2018 and her PhD in theoretical chemistry at Princeton University in 2024. During her graduate studies, she worked in the group of Prof. Salvatore Torquato on extracting microscopic forces from the correlation functions of fluids and the inverse design of disordered hyperuniform systems, which are exotic states of matter that lie between typical liquids and crystals. Her experience with order metrics in chemical physics sparked her interest in disordered active systems in biology. As postdoc at Penn, she works with Profs. Andrea Liu and John Crocker on the "civil engineering" of living cells, i.e., modelling the actin cortex as a dynamic learning system. In her free time, Haina writes music reviews, plays the violin and attends Philadelphia Orchestra concerts.